How to tell if two different network models are statistically significantly different from one another?

Question

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I have two networks A and B. I have the following information:

For A:

• Average node degree of A = 3.2
• Structure of A is like this:

And for B I have this information:

• It's a 5-node Bernoulli random network model without self-loops
• with parameter p = 0.5 (probability for each edge to be in the graph)
• significance level alpha = 0.05
• Approximate distribution of the average node degree for B is as follows:

Is A statistically significantly different from Bernoulli random network model B? How can I assess this? What things should I look at? Does looking at the expected average degree E(G) = (n-1)p help?

Answer 1

[Jean-Karim Heriche]

The typical way to do this is to compare some properties of the graph (e.g. node degree distribution) to the distribution of these properties expected from the model. You may find this tutorial useful. It uses the R package ergm.